MEAN SHIFT SEGMENTATION(meanshift分割算法)

Bucket data structure Mean shift vector reutilization (medium speed up) Local neighborhood inclusion (high speed up)

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OPTIMIZATION TECHNIQUES - EVALUATION


Mean shift segmentation is an advanced and vertisale technique for clustering based segmentation
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MEAN SHIFT ALGORITHM

Kernel density estimation
Kernel density estimation is a non parametric way to estimate the density function of a random variable. It is a popular method for estimating probability density. This is usually called as the Parzen window technique. K(x) : kernel, h: bandwidth parameter (radius), n data point xi , i=1..n in d-dimension space Rd Kernel density estimator for a given set of ddimensional points is
original
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SAMPLES OF MEAN SHIFT SEGMENTATION
(hs,hr ) = (16,4) (hs,hr ) = (16,16)
(hs,hr ) = (8,4)
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OPTIMIZATION TECHNIQUES – PROBLEM
According to the mean shift algorithm, the complexity is O(Tn2), the first step needs the most computationally expensive. It means finding the closet neighbors of a point is the most expensive operation of mean shift method The larger of hs , the slower of processing time. It‘s known „multidimensional range searching“ (Mean Shift Based Clustering in High Dimensions: A Texture

For each point xi Choose a search window Compute the mean shift vector m(xit) Repeat till convergence

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MEAN SHIFT ALGORITHM
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MEAN SHIFT ALGORITHM
MEAN SHIFT SEGMENTATION
Proseminar "Aufgabenstellungen der Bildanalyse und Mustererkennung„
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Thu Huong Nguyen Fakultät Informatik – TU Dresden
CONTENTS
பைடு நூலகம்1. 2.
Overview about Mean Shift Segmentation Mean Shift algorithm
o o
Kernel density estimation Kernel
3. 4.
Mean shift segmentation Applications of Mean Shift
o o o

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SAMPLES OF MEAN SHIFT SEGMENTATION
original (hs,hr ) = (8,4) (hs,hr ) = (8,7)
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SAMPLES OF MEAN SHIFT SEGMENTATION
(hs,hr ) = (8,8) (hs,hr ) = (8,7)

Classification Example.)
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OPTIMIZATION TECHNIQUES - SOLUTIONS
Speed up the computation of mean shift vector Decrease the number of mean shift vector Combination both ----------oOo--------- In „Mean Shift Segmentation Evaluation of Optimization Techniques“ proposed 3 optimization techniques
is in the gradient direction at x of the density estimate using H
1 2 3
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MEAN SHIFT ALGORITHM

The most popularly kernel is Gaussian kernel

And their shadows SK(x) = K(x)
is called Mean shift vector (or sample mean shift)
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MEAN SHIFT ALGORITHM
The mean shift vector computed with kernel G is proportional to the normalized density gradient estimate obtained with the kernel K The mean shift algorithm seeks a mode or local maximum of density of a given distribution Mean shift can be sumed up like this

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MEAN SHIFT SEGMENTATION

Parameter of mean shift segmentation
hs : Spatial resolution parameter Affects the smoothing, connectivity of segments Chosen depending on the size of the image, objects hr : Range resolution parameter Affects the number of segments Should be kept low if contrast is low M : Size of smallest segment Should be chosen based on size of noisy patches
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MEAN SHIFT ALGORITHM

Epanechikov kernel

E(x) = 3∕4 (1 – x2) if |x| ≤ 1 0 else

and its shadow SE(x) = E(x)
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MEAN SHIFT SEGMENTATION
An advanced and versatile technique for clustering-based segmentation Let {xi} i=1…n be the original image points, {zi} i=1… n the points of convergence, and {Li} i=1…n a set of labels Mean Shift Segmentation

For each i = 1…n run the mean shift procedure for xi and store the convergence point in zi . Identify clusters {Cp} p=1…m of convergence points by linking together all zi which are closer than 0,5 from each other in the joint domain. For each i = 1…n assign Li = {p | zi ϵ Cp}. Optional: Eliminate spatial regions smaller than M pixels.

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MEAN SHIFT ALGORITHM

The estimate of the density gradient is defined as the gradient of the kernel density estimate
Setting it to 0 and define g(x) = -K‘(x) we have
Clustering Filtering Visual tracking
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5.
Conclusions
OVERVIEW ABOUT MEAN SHIFT SEGMENTATION

What is Mean Shift ?
For each data point, mean shift defines a window around it and computes the mean of data point. Then it shifts the center of window to the mean and repeats the algorithm till it convergens Mean shift is a nonparametric iterative algorithm or a nonparametric density gradient estimation using a generalized kernel approach Mean shift is the most powerful clustering technique Mean shift is used for image segmentation, clustering, visual tracking, space analysis, mode seeking ...